Understanding the electronic properties of carbon polyprismanes from the $sp^3$ tight-binding model

Carbon polyprismanes are 1D nanostructures that should be classified as diamond-like phases because they (polyprismanes) also consist of the 4-coordinated carbon atoms. A carbon polyprismane contains polygonal atomic rings arranged in layers along the common symmetry axis, at uniform distances from each other. According to previous density functional theory based studies, carbon polyprismanes can exhibit metallic conductivity, which is very unusual for diamond-like phases. In this paper, we present the $sp^3$ tightbinding model based calculations of the band structures for carbon polyprismanes of different diameters and compare the obtained results with their analogs for a 2D square carbon lattice, which can be considered as the limiting case of a carbon polyprismane of infinite diameter. Our results confirm that the $sp^3$ tight-binding model describes the electronic properties of carbon polyprismanes well, since we obtain their band structures over a wide range of parameter values for the proposed model. We believe that such electronic transport characteristics are an intrinsic topological feature of polyprismanes and should also occur in non-carbon polyprismanes.